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Abstract <p>The study examines center-of-pressure dynamics in the anteroposterior direction (CoPx). It is assumed that CoPx dynamics involve two dynamical processes during quiet stance. The first process describes fast postural corrections around the given equilibrium. The second process describes slowly changing equilibrium point which is assumed to be controlled by higher nervous system. We proposed a novel system of coupled stochastic differential equations, double Ornstein-Uhlenbeck process (dOU), where two processes are described in terms of two Ornstein-Uhlenbeck processes (OU). Specifically, the equilibrium point of the fast postural correction OU process is controlled by the slowly evolving equilibrium point OU process. We derived closed forms of correlation and the power spectral density (PSD) functions of the processes. We conducted experiments with three repetitions from eight healthy subjects at four different sensory conditions on rigid and compliant surfaces. We optimized four model parameters in frequency domain by comparing averaged PSD estimates of experimental data and analytical PSD functions at each sensory combination. We found that mean reversion rate <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda\)</EquationSource> </InlineEquation> of the first OU governing postural reflexes around a given equilibrium, was significantly higher on the rigid surface. Consequently, the dynamics of postural sway on rigid surface were predominantly captured by a single OU. Contrarily, on compliant surface, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda\)</EquationSource> </InlineEquation> approached the second OU’s mean reversion rate, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\kappa\)</EquationSource> </InlineEquation>, and we observed a significant increase in its volatility, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\sigma _2\)</EquationSource> </InlineEquation>. Findings suggest that two-level CoPx dynamics become more pronounced under the compliant surface. We showed that dOU is capable of capturing bounded diffusive characteristics of CoPx dynamics.</p>

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Stochastic dynamics of postural sway modeled by double Ornstein Uhlenbeck process

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Naci Barış Yaradanakul,
  • Maryam Hassanpour,
  • Senih Gürses

摘要

Abstract

The study examines center-of-pressure dynamics in the anteroposterior direction (CoPx). It is assumed that CoPx dynamics involve two dynamical processes during quiet stance. The first process describes fast postural corrections around the given equilibrium. The second process describes slowly changing equilibrium point which is assumed to be controlled by higher nervous system. We proposed a novel system of coupled stochastic differential equations, double Ornstein-Uhlenbeck process (dOU), where two processes are described in terms of two Ornstein-Uhlenbeck processes (OU). Specifically, the equilibrium point of the fast postural correction OU process is controlled by the slowly evolving equilibrium point OU process. We derived closed forms of correlation and the power spectral density (PSD) functions of the processes. We conducted experiments with three repetitions from eight healthy subjects at four different sensory conditions on rigid and compliant surfaces. We optimized four model parameters in frequency domain by comparing averaged PSD estimates of experimental data and analytical PSD functions at each sensory combination. We found that mean reversion rate \(\lambda\) of the first OU governing postural reflexes around a given equilibrium, was significantly higher on the rigid surface. Consequently, the dynamics of postural sway on rigid surface were predominantly captured by a single OU. Contrarily, on compliant surface, \(\lambda\) approached the second OU’s mean reversion rate, \(\kappa\) , and we observed a significant increase in its volatility, \(\sigma _2\) . Findings suggest that two-level CoPx dynamics become more pronounced under the compliant surface. We showed that dOU is capable of capturing bounded diffusive characteristics of CoPx dynamics.